babyboogrocks5572
14.04.2020 •
Mathematics
We are given a random collection of 3 cards. (a) What is the conditional probability that all 3 cards are spades, given that the collection contains the ace of spades? Find an approximate decimal. (b) What is the conditional probability that all 3 cards are spades, given that at least one card is a spade? Find an approximate decimal.
Solved
Show answers
More tips
- F Food and Cooking How to Make Delicious Plov: Secrets and Recipes...
- S Sport How to Learn to Pull Up on Monkey Bars?...
- L Leisure and Entertainment Scrapbooking: What is it and Why is it Becoming More Popular?...
- C Computers and Internet Where did torrents.ru move to?...
- B Business and Finance Understanding Cash Flow: What It Is and How It Works...
- C Computers and Internet What Are Peers and Seeds in Torrenting?...
- H Health and Medicine 10 Simple Techniques on How to Boost Your Mood...
- G Goods and services How to Choose the Right High Chair for Your Baby?...
- S Style and Beauty Learn how to tie a keffiyeh on your head like a pro...
Answers on questions: Mathematics
- M Mathematics In a production of Romeo and Juliet, eight actors are considered for the male roles of Romeo, Mercutio, and Benvolio. In how many ways can the director cast the male...
- M Mathematics Apostcard is 4 inches shorter than an envelope. the envelope is 10 inches long. how long is the postcard? the diagram below could be used to solve this problem. write...
- M Mathematics Is triangle dca congruent to triangle bca? explain. (2 points)...
- M Mathematics In which figure is line de parallel to line bc? a)figure 1 b)figure 2 c)figure 3 d)figure 4...
- M Mathematics To achieve maximum coverage of the signal across earth, what type of line should be formed between the point where the satellite is located and the point on earth’s surface...
- M Mathematics Atruck is carrying 10 cars weighing an average of 3,500 pounds each. what is the total weight in tons of the cars on the truck? the total weight of the cars the truck...
- M Mathematics Little sis with homework! =) a student says that the solution of 375 = x – 28 is 347. explain the student’s error and find the correct answer?...
- M Mathematics Solve the equation for x. 3/4 (12x + 4) = 30 a. 3 b. 5 c. 7 d. 12...
- M Mathematics Afurniture maker uses the specification 19.88 ≤ w ≤ 20.12 for the width w in inches of a desk drawer. write the specification as an absolute value inequality....
- M Mathematics The first after the museum of science opened, it had 2,500 visitors. the number of visitors increased by 20% the second week. how many people visited the museum of science...
Ответ:
a) Assuming a standard deck of 52 cards. By definition of conditional probability:
P(3 spades | ace of spades) = P(3 spades AND ace of spades) / P(ace of spades)
We draw 3 cards, so there are (52 choose 3) = 22,100 total possible hands.
There are (1 choose 1)*(51 choose 2) = 1275 possible hands with the ace of spades.
There are (13 choose 3) = 286 possible hands containing 3 spades, and (1 choose 1)*(12 choose 2) = 66 of these contain the ace of spades.
So we have
P(3 spades AND ace of spades) = 66/22,100
P(ace of spades = 1275/22,100
and so
P(3 spades | ace of spades) = 66/1275 = 0.0518
b) By definition:
P(3 spades | at least 1 spade) = P(3 spades AND at least 1 spade) / P(at least 1 spade)
If you draw 3 spades, you already meet the requirement of having at least 1 spade, so
P(3 spades AND at least 1 spade) = P(3 spades)
and we already know there are 286 possible such hands.
The event of getting at least 1 spades is complementary to the event of not getting any spades, meaning
P(at least 1 spade) = 1 - P(no spades)
There are 39 non-spade cards, and so (39 choose 3) = 9139 possible hands not containing spades.
So we find
P(3 spades) = 286/22,100
P(at least 1 spade) = 1 - 9139/22,100 = 12,961/22,100
which means
P(3 spades | at least 1 spade) = 286/12,961 = 0.0221
Ответ:
9) 40,36,_32_,28
10) 5,10,15,__20_
11) 27,_24__,21,18